Test bezier

Bezier.m

@@ -0,0 +1,43 @@
+## Copyright (C) 2018 Stefan
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*- 
+## @deftypefn {Function File} {@var{retval} =} Bezier.py (@var{input1}, @var{input2})
+##
+## @seealso{}
+## @end deftypefn
+
+## Author: Stefan <stefan@Specter>
+## Created: 2018-10-22
+
+function [] = Bezier(v, dim)
+  # result is a dim x 2 matrix
+  # result[i,1] - the x-coordinate
+  # result[i,2] - the y- coordinate 
+  result = zeros(dim, 2);
+  i = 1;
+  # calculate the points from the Bezier curve with deCasteljau
+  # dim - the number of points from the Bezier curve
+  for u = linspace(0,1,dim) 
+    result(i,:) = deCasteljau(v, length(v) - 1, 0, u);
+    i++;
+  endfor
+
+ #  plot the initials points and the Bezier Curve
+ plot (result(1:dim,1), result(1:dim,2), 'r','LineWidth',2)
+ hold
+ plot(v(:,1), v(:,2),'LineWidth',2)
+ title('Bezier Curve for given points')
+endfunction

GaussJordan.py

@@ -0,0 +1,43 @@
+import numpy as np
+# calculate the inverse of the matrix A using Gauss-Jordan algorithm
+def GaussJordan (A):
+    (n, n) = A.shape
+    B = np.eye(n)
+
+    # Assume A has an inverse matrix
+    success = 1
+
+    if np.linalg.det(A) == 0:
+        # A cannot be reversed
+        B = np.empty(n)
+        success = 0
+        return
+
+    # merge the two matrices
+    Ae = np.concatenate((A, B.T), axis=1)
+    for i in range (0, n):
+        if Ae[i, i] == 0:
+            B = np.empty(n)
+            success = 0
+            return
+         # make the pivot position to one (as in the eye matrix)
+        Ae[i, :] = Ae[i, :] / Ae[i, i]
+
+        #form zeros above and under the main diagonal in the
+        # first half and calculate the inverse in the second half
+        for j in range(0, n):
+            if i != j:
+                Ae[j, :] = Ae[j, :] - Ae[i, :] * Ae[j, i]
+
+    #extract the inverse of matrix A from the augmented matrix
+    B = Ae[:, n : 2 * n ]
+    return (B, success)
+
+
+# example for a 4x4 matrix
+A = np.random.rand(4,4)
+(inv, success) = GaussJordan(A)
+print "The inverse using Gauss-Jordan is:"
+print inv
+print "The inverse using inv from linalg is:"
+print np.linalg.inv(A)

deCasteljau.m

@@ -0,0 +1,32 @@
+## Copyright (C) 2018 Stefan
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*- 
+## @deftypefn {Function File} {@var{retval} =} deCasteljau (@var{input1}, @var{input2})
+##
+## @seealso{}
+## @end deftypefn
+
+## Author: Stefan <stefan@Specter>
+## Created: 2018-10-22
+
+# Returns a point from the Bezier curve
+function [result] = deCasteljau (v,i,j,t)
+  if i == 0
+    result = v(j + 1, :);
+  else
+    result = (1 - t) * deCasteljau(v,i - 1,j,t) + t * deCasteljau(v,i - 1, j + 1,t);   
+  endif
+endfunction

matlab/ad-hoc/tests/Bezier.m

@@ -0,0 +1,43 @@
+## Copyright (C) 2018 Stefan
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*- 
+## @deftypefn {Function File} {@var{retval} =} Bezier.py (@var{input1}, @var{input2})
+##
+## @seealso{}
+## @end deftypefn
+
+## Author: Stefan <stefan@Specter>
+## Created: 2018-10-22
+
+function [] = Bezier(v, dim)
+  # result is a dim x 2 matrix
+  # result[i,1] - the x-coordinate
+  # result[i,2] - the y- coordinate 
+  result = zeros(dim, 2);
+  i = 1;
+  # calculate the points from the Bezier curve with deCasteljau
+  # dim - the number of points from the Bezier curve
+  for u = linspace(0,1,dim) 
+    result(i,:) = deCasteljau(v, length(v) - 1, 0, u);
+    i++;
+  endfor
+
+ #  plot the initials points and the Bezier Curve
+ plot (result(1:dim,1), result(1:dim,2), 'r','LineWidth',2)
+ hold
+ plot(v(:,1), v(:,2),'LineWidth',2)
+ title('Bezier Curve for given points')
+endfunction

matlab/ad-hoc/tests/deCasteljau.m

@@ -0,0 +1,32 @@
+## Copyright (C) 2018 Stefan
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*- 
+## @deftypefn {Function File} {@var{retval} =} deCasteljau (@var{input1}, @var{input2})
+##
+## @seealso{}
+## @end deftypefn
+
+## Author: Stefan <stefan@Specter>
+## Created: 2018-10-22
+
+# Returns a point from the Bezier curve
+function [result] = deCasteljau (v,i,j,t)
+  if i == 0
+    result = v(j + 1, :);
+  else
+    result = (1 - t) * deCasteljau(v,i - 1,j,t) + t * deCasteljau(v,i - 1, j + 1,t);   
+  endif
+endfunction

matlab/ad-hoc/tests/testBezier.m

@@ -0,0 +1,37 @@
+# USES Bezier.m and DeCasteljau.m
+
+# Test 00
+# Bezier curve for n = 3
+figure
+A = [1 1; 2 3; 4 3; 3 1]
+Bezier(A, 250)
+
+# Test 01
+# Bezier curve for n = 3
+# Reason: 1st and 4th points are the same
+figure
+A = [1 1; 2 3; 4 3; 1 1];
+Bezier(A,250)
+
+# Test 02
+# Bezier curve for n = 3 
+# Reason: Repeated 2 points
+figure
+A = [1 1; 2 3; 2 3; 3 1];
+Bezier(A,250)
+
+# Test 03
+# Bezier curve for n = 3
+# Reason: Modified the repeated points
+figure
+A = [1 1; 2 3; 2.2 3; 3 1];
+Bezier(A,250)
+
+# Test 04
+# Bezier curve for n = 3
+# Reason: One data point altered
+figure
+A = [1 1; 2 1; 4 3; 3 1]
+Bezier (A, 250)
+
+

python/Gershgorin.py

@@ -0,0 +1,41 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def Gershgorin (A):
+    # A must be a square matrix
+    (m,n)  = A.shape
+    if m != n:
+        print "You must introduce a square matrix"
+        return
+
+    plt.axes()
+    # For each row:
+    for i in range (0, n):
+        # the circle has the center in (h, k) where
+        # h is the real part of A(i,i) and k is the real part of A(i,i)
+        h = np.real(A[i,i])
+        k = np.imag(A[i,i])
+        plt.plot(h, k, marker='x', markersize=5, color="blue")
+
+        # the radius of the circle is the sum of 
+        # norm of the elements in the row where i != j
+
+        r = 0
+        for j in range (0,n):
+            if i != j:
+                r = r + np.linalg.norm(A[i,j])
+        # plot the circle
+        circle = plt.Circle((h, k), r, fill = False)
+        plt.gca().add_patch(circle)        
+
+    eigenval = np.linalg.eigvals(A)
+   # plot the eigenvalues of the matrix
+    for x in eigenval:
+        plt.plot(np.real(x), np.imag(x), marker='o', markersize=5, color="red")
+
+    plt.axis('scaled')
+    plt.show()
+# example for a 3x3 matrix
+A = np.random.rand(3,3)
+print A
+Gershgorin(A)

testBezier.m

@@ -0,0 +1,37 @@
+# USES Bezier.m and DeCasteljau.m
+
+# Test 00
+# Bezier curve for n = 3
+figure
+A = [1 1; 2 3; 4 3; 3 1]
+Bezier(A, 250)
+
+# Test 01
+# Bezier curve for n = 3
+# Reason: 1st and 4th points are the same
+figure
+A = [1 1; 2 3; 4 3; 1 1];
+Bezier(A,250)
+
+# Test 02
+# Bezier curve for n = 3 
+# Reason: Repeated 2 points
+figure
+A = [1 1; 2 3; 2 3; 3 1];
+Bezier(A,250)
+
+# Test 03
+# Bezier curve for n = 3
+# Reason: Modified the repeated points
+figure
+A = [1 1; 2 3; 2.2 3; 3 1];
+Bezier(A,250)
+
+# Test 04
+# Bezier curve for n = 3
+# Reason: One data point altered
+figure
+A = [1 1; 2 1; 4 3; 3 1]
+Bezier (A, 250)
+
+